A calculation method for surrounding rock strain distribution considering the effect of pore pressure

Abstract

The present invention discloses a calculation method for the strain distribution of surrounding rock considering the pore pressure effect. The steps are as follows: Step S1, establish a geometric model of the target formation; Step S2, obtain the basic parameters of the target formation; Step S3, establish a calculation model for the strain distribution of surrounding rock considering the pore pressure effect. When establishing the model, comprehensively consider the flow properties of formation fluids under stress and the changes in rock physical properties; Step S4, substitute the basic parameters of the target formation obtained in Step S2 into the calculation model established in Step S3 to calculate the strain distribution of the surrounding rock of the target formation. The method of the present invention fully considers multiple factors such as the change in rock permeability under the stress of the surrounding rock, the displacement of rock particles in different directions, and the strain of the rock skeleton in different directions, enabling the calculated surrounding rock strain distribution to be more in line with the actual situation and improving the accuracy and reliability of the calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas exploitation, in particular to a calculation method for the strain distribution of surrounding rock considering the effect of pore pressure. Background Art

[0002] Shale oil and gas and tight oil and gas are natural gas resources extracted from dense rock formations. Compared with conventional natural gas, their gas production rate is relatively stable and can be exploited for a long time. Shale oil and gas and tight oil and gas are mainly distributed in dark mudstone or high-carbon mudstone, and their accumulation methods in mudstone are adsorption or free state. Shale oil and gas resources in China are relatively rich. However, due to the characteristics of low permeability and low porosity of shale oil and gas reservoirs, their exploitation requires horizontal well drilling technology and large-scale hydraulic fracturing technology.

[0003] While hydraulic fracturing technology enhances the productivity of reservoirs, it also has certain impacts on the formation in the fracturing area, leading to the collapse and instability of the wellbore walls of adjacent platform wells, mainly manifested in two aspects: on the one hand, hydraulic fractures communicate with natural fractures to form a fracture network, making it easier for various fluids to invade the formation along the fracture network, resulting in water-rock interaction and thus weakening the rock strength of the formation; on the other hand, an artificial fracture area will be generated after hydraulic fracturing operations, and the propagation of artificial fractures will lead to the redistribution of in-situ stress and pore pressure in the reservoir, having a great impact on the drilling construction in progress in the fracturing area. If the drilling construction design in the fracturing area still refers to the data of adjacent wells, it will increase the drilling risk. For example, in a certain shale oil and gas and tight oil and gas field, the actual drilling mud density of the vertical well being drilled adjacent to the fracturing well increased by more than 0.15 g / cm 3 ³ compared with the well not affected by fracturing, accompanied by downhole complex situations such as gas invasion, overflow, and water production (fracturing fluid pollution). Therefore, there are the following problems in the shale oil and gas and tight oil and gas exploitation technology: the influence of hydraulic fracturing operations on pore pressure leads to the redistribution of pore pressure, the mechanism of the action of pore pressure on the strain and deformation of the surrounding rock of the well is not very clear, the rationality of the calculation is not considered, and whether the existing models are suitable for the strain distribution of the surrounding rock after hydraulic fracturing operations, etc., and it cannot provide effective reference for engineering. Summary of the Invention

[0004] Aiming at the technical defect that the influence of pore pressure is not considered in the calculation process of the strain and deformation of the surrounding rock of the well during fracturing operations in the prior art, the present invention provides a calculation method for the strain distribution of surrounding rock considering the effect of pore pressure.

[0005] The calculation method for the strain distribution of surrounding rock considering the effect of pore pressure provided by the present invention is as follows:

[0006] S1. Establish a geometric model of the target formation.

[0007] S2. Obtain the basic parameters of the target formation; the basic parameters include the formation Young's modulus, Poisson's ratio, maximum horizontal principal strain, minimum horizontal principal strain, overburden pressure, formation pressure, formation density, pore fluid density, wellbore fluid column pressure, initial shale porosity, initial shale permeability, and wellbore diameter.

[0008] S3. Establish a calculation model for the strain distribution of the surrounding rock considering the effect of pore pressure; when establishing the calculation model, comprehensively consider the flow properties of formation fluids and the changes in rock physical properties under stress; the calculation model is as follows:

[0009]

[0010] In the formula: is the porosity; C w is the fluid compressibility, MPa -1 ; p p is the pore pressure of the shale formation, MPa; t is the time, s; C s is the rock skeleton compressibility, MPa -1 ; μ is the fluid viscosity, mPa·s; K is the permeability, μm 2 ; p w is the fluid pressure, MPa; ρ w is the fluid density, g / cm 3 ; H is the pressure gradient, m; ε V is the rock skeleton strain.

[0011] The permeability K is calculated by the following formula:

[0012]

[0013] In the formula: is the initial porosity; K0 is the initial permeability, μm 2 ; K m is the bulk modulus of volume compression of the skeleton, MPa; Δp p is the change in pore pressure, MPa.

[0014] The rock skeleton strain ε V is calculated by the following formula:

[0015]

[0016] In the formula: u, v, w are the displacements of the rock skeleton particles in the x, y, z directions; G is the shear modulus, MPa; m is the Poisson's ratio; F x is the sum of the strains of the rock skeleton particles in the x direction; F y is the sum of the strains of the rock skeleton particles in the y direction; F z is the sum of the strains of the rock skeleton particles in the z direction.

[0017] The strain of the rock skeleton particles in the x, y, and z directions and F x , F y , F z The calculation formulas are as follows:

[0018]

[0019] F x = F z cosθ

[0020] F y = F z sinθ

[0021] In the formula: R is the wellbore radius, m; r is the distance from the wellbore center, m; θ is the wellbore circumference angle, rad; σ r is the radial strain, MPa; σ H is the maximum horizontal in-situ stress, MPa; σ h is the minimum horizontal in-situ stress, MPa; x, y are the positions of the mass points.

[0022] S4. Substitute the basic parameters of the target formation obtained in step S2 into the calculation model established in step S3 to calculate the surrounding rock strain distribution of the target formation.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0024] The method of the present invention considers the influence of pore pressure on the surrounding rock strain distribution, specifically considers the changes in rock permeability under the action of surrounding rock stress, the displacements of rock particles in different directions, the strains of the rock skeleton in different directions, etc. It can make the calculated surrounding rock strain distribution more in line with the actual situation, improve the accuracy and reliability of the calculation, and provide technical support for oil and gas development.

[0025] Other advantages, objectives, and features of the present invention will be partially reflected by the following description, and partially will be understood by those skilled in the art through the research and practice of the present invention. Brief Description of the Drawings

[0026] Figure 1 It is a comparison curve graph of the circumferential stress distribution of the wellbore in the embodiment.

[0027] Figure 2 It is a wellbore strain distribution diagram under the condition of a simulated formation pore pressure of 30 MPa in the embodiment.

[0028] Figure 3 It is a wellbore strain distribution diagram under the condition of a simulated formation pore pressure of 35 MPa in the embodiment.

[0029] Figure 4 The borehole strain distribution diagram under the condition of a simulated formation pore pressure of 40 MPa for the embodiment.

[0030] Figure 5 The borehole strain distribution diagram under the condition of a simulated formation pore pressure of 45 MPa for the embodiment. Specific Embodiments

[0031] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only for the purpose of illustrating and explaining the present invention, and are not intended to limit the present invention.

[0032] In the method of the present invention, in step S3, a calculation model for the strain distribution of the surrounding rock considering the action of pore pressure is established, and the specific process is as follows:

[0033] First, formation fluids exist in the pores and matrix of the borehole surrounding rock. During the fluid seepage process, the generated fluid pressure will cause deformation of the rock skeleton, resulting in displacement of the skeleton particles with a certain velocity. The absolute velocity of fluid movement can be expressed as:

[0034]

[0035] In the formula: is the absolute velocity of fluid movement, m / s; is the relative velocity of the fluid, m / s; is the relative velocity of the rock mass skeleton particles, m / s;

[0036] The relative velocity of the rock mass skeleton particles can be expressed as:

[0037]

[0038] In the formula: u, v, and w are the displacements of the rock skeleton particles in the x, y, and z directions, m; t is the time, s.

[0039] The movement velocity of the single-phase fluid can be obtained according to Darcy's law:

[0040]

[0041] In the formula: is the porosity, dimensionless; μ is the fluid viscosity, mPa·s; K is the permeability, μm 2 ; p w is the fluid pressure, MPa; ρ w is the fluid density, g / cm 3 ; g is the acceleration of gravity, m / s 2 ; H is the pressure gradient, m.

[0042] According to the law of conservation of mass, the change in the mass of fluid within the infinitesimal element per unit time is equal to the difference between the mass of fluid flowing into and out of the infinitesimal element. Thus, the continuity equation for pore fluid can be obtained as follows:

[0043]

[0044] Substituting equations (2) and (3) into equation (4), the continuity equation for pore fluid can be obtained:

[0045]

[0046] In the formula: ε V is the strain of the rock skeleton, dimensionless.

[0047] Similarly, the continuity equation for the skeleton can be obtained as follows:

[0048]

[0049] In the formula: ρ s is the density of the rock mass skeleton, g / cm 3 .

[0050] By superimposing equations (5) and (6), the continuity equation for the entire porous medium can be obtained

[0051]

[0052] When the temperature effect is not considered, the density of the pore fluid is related to the pore pressure, and the relationship is as follows:

[0053]

[0054] In the formula: ρ0 is the initial fluid density, g / cm 3 ; p0 is the initial fluid pressure, MPa; p p is the pore pressure of the shale formation, MPa; C w is the fluid compressibility, MPa -1 .

[0055] Since the fluid density and pore pressure change with time, taking the partial derivative with respect to time gives:

[0056]

[0057] Similarly, the state equation of the rock mass skeleton particles can be expressed as:

[0058]

[0059] In the formula: C s is the compressibility of the rock skeleton, MPa -1 .

[0060] Substitute Equation (9) and Equation (10) into Equation (7), and the calculation model of the surrounding rock strain distribution considering the pore pressure effect can be obtained:

[0061]

[0062] In a specific embodiment, when the pore pressure is not applied, the shale formation and the wellbore are mainly affected by the maximum horizontal principal stress, the minimum horizontal principal stress, and the drilling fluid column pressure. The combined action of these forces will cause stress concentration around the wellbore. Due to the symmetry of the wellbore, a quarter of the wellbore is selected as an example in this instance. A square with a side length of 5 m is selected as the surrounding rock of the well in the geometric model, and a quarter circle with a radius of about 0.15 m is intercepted at the square corner as the wellbore radius. The formation mechanical parameters of the reservoir are based on the basic parameters before fracturing in a certain shale oil and gas and tight oil and gas work area in southern Sichuan. Therefore, in order to balance the formation pressure, the wellbore fluid column pressure is set to 26 MPa, and the basic parameters set in the numerical model are shown in Table 1.

[0063] Table 1. Basic parameters set in the numerical model

[0064] Parameter Name Value Parameter Name Value Formation Young's Modulus (GPa) 30 <![CDATA[Formation density (kg / m 3 )]]> 2450 Poisson's Ratio 0.3 <![CDATA[Pore fluid density (kg / m 3 )]]> 1000 Maximum Horizontal Principal Strain (MPa) 45 Wellbore Fluid Column Pressure (MPa) 26 Minimum Horizontal Principal Strain (MPa) 35 Initial Shale Porosity (%) 5 Overburden Pressure (MPa) 40 <![CDATA[Initial shale permeability (μm 2 )]]> <![CDATA[1×10 -5 > Formation Pressure (MPa) 25 Hole Diameter (mm) 311.2

[0065] The circumferential conversion formula and the theoretical calculation formula are given below. By comparing the calculation results, the accuracy of this model can be verified.

[0066] σ θ = σ x sin 2 θ + σ y cos 2 θ - τ xy sin(2θ) (12)

[0067] σ θ = (σ H + σ h ) - 2(σ H - σ h )cos(2θ) (13)

[0068] In the formula: σ θ is the circumferential stress, MPa; θ is the wellbore angle, rad; σ x , σ y are the normal stress components in the x and y directions, MPa; τ xy is the shear stress component, MPa.

[0069] According to the basic parameters in Table 1, the model after the in-situ stress balance is solved, and the curve of the circumferential stress varying with the wellbore angle is obtained, as shown in Figure 1As shown, the specified stress value is: tensile stress is positive and compressive stress is negative. It can be seen from the figure that the in-situ stress exerts pressure on the wellbore, and the circumferential stress shows periodic changes with the increase of the wellbore circumference angle. The numerical solution of the circumferential stress is in good agreement with the analytical solution, which proves that the calculation result of the surrounding rock strain distribution calculation model established by the present invention is relatively accurate.

[0070] In another embodiment, the method for calculating the surrounding rock strain distribution considering the pore pressure effect of the present invention is used to calculate the surrounding rock strain. In this embodiment, due to the symmetry of the wellbore, a quarter of the wellbore is selected as an example. A square with a side length of 5 m is selected as the surrounding rock of the wellbore in the geometric model, and a quarter circle with a radius of about 0.15 m is intercepted at the square corner as the wellbore radius. The formation mechanical parameters of the reservoir are based on the basic parameters before fracturing in a shale oil and gas and tight oil and gas field in southern Sichuan. The pore pressure of the shale formation is set to 25 MPa. Therefore, in order to balance the formation pressure, the wellbore liquid column pressure is set to 26 MPa. The basic parameters set in the numerical model are shown in Table 2.

[0071] Table 2. Basic parameters set in the numerical model

[0072] Parameter Name Value Parameter Name Value Formation Young's Modulus (GPa) 310 <![CDATA[Formation density (kg / m 3 )]]> 2450 Poisson's Ratio 0.29 <![CDATA[Pore fluid density (kg / m 3 )]]> 1000 Maximum Horizontal Principal Strain (MPa) 44 Wellbore Fluid Column Pressure (MPa) 26 Minimum Horizontal Principal Strain (MPa) 32 Initial Shale Porosity (%) 5 Overburden Pressure (MPa) 41 <![CDATA[Initial shale permeability (μm 2 )]]> <![CDATA[5×10 -5 > Formation Pressure (MPa) 25 Hole Diameter (mm) 333..4

[0073] Substitute the basic parameters in Table 2 into the calculation model for the surrounding rock strain distribution considering the pore pressure effect, and the obtained surrounding rock strain distribution results are as Figures 2 - 5 shown. Figures 2 - 5 They are the wellbore strain distribution diagrams under the conditions of simulated formation pore pressures of 30 MPa, 35 MPa, 40 MPa, and 45 MPa respectively.

[0074] In summary, the method of the present invention can more accurately and reasonably calculate the surrounding rock strain distribution considering the pore pressure effect by comprehensively considering the effect of pore pressure on the strain and deformation of the surrounding rock of the wellbore, ensure the exploitation of shale oil and gas and tight oil and gas, and provide an effective reference for the surrounding rock strain distribution considering the pore pressure effect on site.

[0075] The above are only preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the disclosed technical content within the scope of the technical solution of the present invention. However, as long as the content does not depart from the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A calculation method for the strain distribution of surrounding rock considering the effect of pore pressure, characterized in that, It includes the following steps: S1. Establish a geometric model of the target formation; S2. Obtain the basic parameters of the target formation; S3. Establish a calculation model for the strain distribution of the surrounding rock considering the pore pressure effect; The calculation model is as follows: In the formula: is porosity; C w is the fluid compressibility, MPa -1 ; p p is the pore pressure of the shale formation, MPa; t is time, s; C s is the rock matrix compressibility, MPa -1 ; μ is the fluid viscosity, mPa·s; K is the permeability, μm 2 ; p w is the fluid pressure, MPa; ρ w is the fluid density, g / cm 3 ; H is the pressure gradient, m; ε V is the rock matrix strain; S4. Substitute the basic parameters of the target formation obtained in step S2 into the calculation model established in step S3 to calculate the strain distribution of the surrounding rock of the target formation.

2. The method for calculating the surrounding rock strain distribution considering the pore pressure effect according to claim 1, wherein, In step S2, obtaining the basic parameters of the target formation includes the Young's modulus of the formation, Poisson's ratio, maximum horizontal principal strain, minimum horizontal principal strain, overburden pressure, formation pressure, formation density, pore fluid density, wellbore liquid column pressure, initial shale porosity, initial shale permeability, and wellbore diameter.

3. The calculation method of surrounding rock strain distribution considering the pore pressure effect according to claim 1, characterized in that, The permeability K is calculated by the following formula: In the formula: is the initial porosity; K0 is the initial permeability, μm 2 ; K m is the bulk modulus of volume compression of the skeleton, MPa; Δp p is the change in pore pressure, MPa.

4. The method for calculating the surrounding rock strain distribution considering the pore pressure effect according to claim 1, wherein The strain ε of the rock skeleton V is calculated by the following formula: Where: u, v, and w are the displacements of the rock skeleton particles in the x, y, and z directions; G is the shear modulus, in MPa; m is the Poisson's ratio; F x is the sum of the strains of the rock skeleton particles in the x direction; F y is the sum of the strains of the rock skeleton particles in the y direction; F z is the sum of the strains of the rock skeleton particles in the z direction.

5. The method for calculating the surrounding rock strain distribution considering the pore pressure effect according to claim 4, characterized in that, The strain and F of the rock skeleton particles in the x, y, and z directions x and F y and F z The calculation formulas are as follows: F x = F z cosθ F y = F z sinθ Where: R is the wellbore radius, m; r is the distance from the wellbore center, m; θ is the wellbore circumference angle, rad; σ r is the radial strain, MPa; σ H is the maximum horizontal in-situ stress, MPa; σ h is the minimum horizontal in-situ stress, MPa; x, y are the positions of the mass points.

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